基本信息
讲座题目：Some fundamentals of financial mathematics and recent research progress in American option pricing under regime switching models
报告人：诸颂平教授 伍伦贡大学
报告地点：数学楼第一报告厅
校内联系人:韩月才 hanyc@jlu.edu.cn
讲座内容及时间
课程摘要
As one of the most well-known examples in which mathematics has been successfully applied to social sciences, financial mathematics is a dynamic and vibrant research field where academics and practitioners in finance industry are constantly trying to broaden such applications. In this short course, I shall first, as Part 1 of the two parts, discuss some fundamental issues that quite often confuse beginners such as freshly enrolled PhD students or even ECRs (Earlier Career Researchers) in this field.
In Part 2, I shall present a recent research progress in adopting regime-switching model to price American put options: a generalized and highly efficient integral equation formulation has been developed with a goal of improving computational efficiency in mind, particularly when the number of regimes is large. Our achieved high efficiency is based on a newly proved theorem, which facilitates the decoupling of simultaneously coupled partial differential equation (PDE) sets so that they can be solved recursively at the numerical solution stage. Such a high efficiency is of course also fuelled further by the integral equation approach being characterized with its excellent trade-off between maximizing analytical tractability and minimizing numerical discretization. Some numerical examples are provided to demonstrate the implementation of the new approach and its efficiency.
To suit a broad range of students, the emphasis and majority of time during the five-lecture series will be on Part 1, so that the whole series contains some very fundamental concepts in financial mathematics (for undergraduate students), some principles of conducting scientific research (for master students) as well as some brief discussions and presentations of the most recent research outcomes from my research group at UoW (for master and PhD students).
报告人简介
诸颂平教授是澳大利亚伍伦贡大学应用数学系资深教授。他于1987年12月毕业于密歇根大学并获博士学位，累计在国际期刊和会议论文集上发表论文200 余篇，吸引了澳大利亚研究理事会（ARC）和私营企业超过 200 万美元的资金支持。此外，诸颂平教授共组织了两次国际会议，并应邀在多个国际会议上发言。诸颂平教授的研究工作得到了国内外的广泛认可，据ISI Web of Science 数据显示，他的论文总引用次数超过 2000 次，H指数为27。
